Coherence Resonance in a Double-Gyre Model of the Kuroshio Extension

Stefano Pierini Dipartimento di Scienze per l’Ambiente, Università di Napoli Parthenope, Naples, Italy

Search for other papers by Stefano Pierini in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The effect of stochastic winds on the intrinsic low-frequency variability of the Kuroshio Extension (KE) is analyzed through a double-gyre (DG) model forced by a steady climatological wind plus an idealized Ornstein–Uhlenbeck wind noise. A DG model of the KE bimodality, whose results compare well to altimeter data, is first shown to be an excitable system. In fact, the relaxation oscillation (forced by steady winds) with decadal time scale that describes the bimodality is recognized to be an internal mode of the system, which can be excited also in a dissipative parameter range (PR) in which it does not arise spontaneously, provided appropriate initial conditions are chosen. It is then shown that, if the additive wind noise is included in the forcing, the actual excitation of the relaxation oscillation in PR occurs if the noise is red with a decorrelation time greater than a minimum time scale ranging from 1 month to 1 year, depending on the dissipation. This behavior, known as “coherence resonance,” is likely to be paradigmatic of the low-frequency variability of western boundary current extensions of intrinsic origin, when it is in the form of relaxation oscillations resulting from a homoclinic bifurcation. General considerations concerning the interpretation of model results obtained within different parameter ranges are applied to this study.

Corresponding author address: Stefano Pierini, Dipartimento di Scienze per l’Ambiente, Università di Napoli “Parthenope,” Centro Direzionale - Isola C4, 80143 Naples, Italy. Email: stefano.pierini@uniparthenope.it

Abstract

The effect of stochastic winds on the intrinsic low-frequency variability of the Kuroshio Extension (KE) is analyzed through a double-gyre (DG) model forced by a steady climatological wind plus an idealized Ornstein–Uhlenbeck wind noise. A DG model of the KE bimodality, whose results compare well to altimeter data, is first shown to be an excitable system. In fact, the relaxation oscillation (forced by steady winds) with decadal time scale that describes the bimodality is recognized to be an internal mode of the system, which can be excited also in a dissipative parameter range (PR) in which it does not arise spontaneously, provided appropriate initial conditions are chosen. It is then shown that, if the additive wind noise is included in the forcing, the actual excitation of the relaxation oscillation in PR occurs if the noise is red with a decorrelation time greater than a minimum time scale ranging from 1 month to 1 year, depending on the dissipation. This behavior, known as “coherence resonance,” is likely to be paradigmatic of the low-frequency variability of western boundary current extensions of intrinsic origin, when it is in the form of relaxation oscillations resulting from a homoclinic bifurcation. General considerations concerning the interpretation of model results obtained within different parameter ranges are applied to this study.

Corresponding author address: Stefano Pierini, Dipartimento di Scienze per l’Ambiente, Università di Napoli “Parthenope,” Centro Direzionale - Isola C4, 80143 Naples, Italy. Email: stefano.pierini@uniparthenope.it

Save
  • Benzi, R., A. Sutera, and A. Vulpiani, 1981: The mechanism of stochastic resonance. J. Phys., 14A , L453L457.

  • Benzi, R., G. Parisi, A. Sutera, and A. Vulpiani, 1982: Stochastic resonance in climatic change. Tellus, 34 , 1016.

  • Caballero, R., S. Jewson, and A. Brix, 2002: Long memory in surface air temperature: Detection, modeling, and application to weather derivative valuation. Climate Res., 21 , 127140.

    • Search Google Scholar
    • Export Citation
  • Dijkstra, H. A., 2005: Nonlinear Physical Oceanography: A Dynamical Systems Approach to the Large Scale Ocean Circulation and El Niño. Springer, 532 pp.

    • Search Google Scholar
    • Export Citation
  • Dijkstra, H. A., and M. Ghil, 2005: Low-frequency variability of the large-scale ocean circulation: A dynamical systems approach. Rev. Geophys., 43 , RG3002. doi:10.1029/2002RG000122.

    • Search Google Scholar
    • Export Citation
  • Ditlevsen, P. D., K. K. Andersen, and A. Svensson, 2007: The DO-climate events are probably noise induced: Statistical investigation of the claimed 1470 years cycle. Climate Past, 3 , 129134.

    • Search Google Scholar
    • Export Citation
  • Frankcombe, L. M., H. A. Dijkstra, and A. S. Von der Heydt, 2009: Noise induced multidecadal variability in the North Atlantic: Excitation of normal modes. J. Phys. Oceanogr., 39 , 220233.

    • Search Google Scholar
    • Export Citation
  • Gammaitoni, L., P. Hanggi, P. Jung, and F. Marchesoni, 1998: Stochastic resonance. Rev. Mod. Phys., 70 , 223287.

  • Ganopolski, A., and S. Rahmstorf, 2002: Abrupt glacial climate changes due to stochastic resonance. Phys. Rev. Lett., 88 , 038501. doi:10.1103/PhysRevLett.88.038501.

    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., 1976: Stochastic climate models. Part I. Theory. Tellus, 28 , 473484.

  • Imkeller, P., and J. S. Von Storch, Eds.,. 2001: Stochastic Climate Models. Birkhäuser, 398 pp.

  • Lindner, B., J. Garcìa-Ojalvo, A. Neiman, and L. Schimansky-Geier, 2004: Effects of noise in excitable systems. Phys. Rep., 392 , 321424.

    • Search Google Scholar
    • Export Citation
  • Nicolis, C., 1982: Stochastic aspects of climatic transitions— Responses to periodic forcing. Tellus, 34 , 19.

  • Pelletier, J. D., 2003: Coherence resonance and ice ages. J. Geophys. Res., 108 , 4645. doi:10.1029/2002JD003120.

  • Pérez-Muñuzuri, V., R. Deza, K. Fraedrich, T. Kunz, and F. Lunkeit, 2005: Coherence resonance in an atmospheric global circulation model. Phys. Rev. E., 71 , 065602. doi:10.1103/PhysRevE.71.065602.

    • Search Google Scholar
    • Export Citation
  • Pierini, S., 2006: A Kuroshio Extension System model study: Decadal chaotic self-sustained oscillations. J. Phys. Oceanogr., 36 , 16051625.

    • Search Google Scholar
    • Export Citation
  • Pierini, S., 2008: On the crucial role of basin geometry in double-gyre models of the Kuroshio Extension. J. Phys. Oceanogr., 38 , 13271333.

    • Search Google Scholar
    • Export Citation
  • Pierini, S., H. A. Dijkstra, and A. Riccio, 2009: A nonlinear theory of the Kuroshio Extension bimodality. J. Phys. Oceanogr., 39 , 22122229.

    • Search Google Scholar
    • Export Citation
  • Pikovsky, A. S., and J. Kurths, 1997: Coherence resonance in noise-driven excitable systems. Phys. Rev. Lett., 78 , 775778.

  • Primeau, F., and D. Newman, 2008: Elongation and contraction of the western boundary current extension in a shallow-water model: A bifurcation analysis. J. Phys. Oceanogr., 38 , 14691485.

    • Search Google Scholar
    • Export Citation
  • Qiu, B., and S. Chen, 2005: Variability of the Kuroshio Extension jet, recirculation gyre, and mesoscale eddies on decadal time scales. J. Phys. Oceanogr., 35 , 20902103.

    • Search Google Scholar
    • Export Citation
  • Rahmstorf, S., 2003: Timing of abrupt climate change: A precise clock. Geophys. Res. Lett., 30 , 1510. doi:10.1029/2003GL017115.

  • Roulston, M. S., and J. D. Neelin, 2000: The response of an ENSO model to climate noise, weather noise and intraseasonal forcing. Geophys. Res. Lett., 27 , 37233726.

    • Search Google Scholar
    • Export Citation
  • Simonnet, E., M. Ghil, and H. A. Dijkstra, 2005: Homoclinic bifurcations in the quasi-geostrophic double-gyre circulation. J. Mar. Res., 63 , 931956.

    • Search Google Scholar
    • Export Citation
  • Sura, P., K. Fraedrich, and F. Lunkeit, 2001: Regime transitions in a stochastically forced double-gyre model. J. Phys. Oceanogr., 31 , 411426.

    • Search Google Scholar
    • Export Citation
  • Sushama, L., M. Ghil, and K. Ide, 2007: Spatio-temporal variability in a mid-latitude ocean basin subject to periodic wind forcing. Atmos.–Ocean, 45 , 227250. doi:10.3137/ao.450404.

    • Search Google Scholar
    • Export Citation
  • Tsimring, L. S., and A. Pikovsky, 2001: Noise-induced dynamics in bistable systems with delay. Phys. Rev. Lett., 87 , 250602. doi:10.1103/PhysRevLett.87.250602.

    • Search Google Scholar
    • Export Citation
  • Von Storch, H., J. S. Von Storch, and P. Müller, 2000: Noise in the climate system—Ubiquitous, constitutive and concealing. Mathematics Unlimited: 2001 and Beyond, Part II, B. Engquist and W. Schmid, Eds., Springer-Verlag, 1179–1194.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 140 47 7
PDF Downloads 70 24 4